Oscillations

JEE Main level, single correct, medium

150 of 194

Question 150 of 194

Two simple pendulums having lengths l1l_1 and l2l_2 with negligible string mass undergo angular displacements θ1\theta_1 and θ2\theta_2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

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Answer: (D) θ1l2=θ2l1\theta_1 l_2=\theta_2 l_1

ω=gℓα=−ω2θ∴ gℓ1θ1=gℓ2θ2⇒θ1ℓ2=θ2ℓ2\begin{aligned} & \omega=\sqrt{\frac{\mathrm{g}}{\ell}} \\ & \alpha=-\omega^2 \theta \\ & \therefore \frac{\mathrm{~g}}{\ell_1} \theta_1=\frac{\mathrm{g}}{\ell_2} \theta_2 \\ & \Rightarrow \theta_1 \ell_2=\theta_2 \ell_2\end{aligned}

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